calculus
posted by thomas .
just wondering if someoen could help me with this limit..:
lim arctan[(x^2  4)/(3x^26x)]
x>2

My first step in doing limits is to sub in the approach value, this will give me Lim arctan (0/0)
This just about guarantees that the algebraic expression will factor and the offending factor will cancel.
Sure enough
lim arctan[(x^2  4)/(3x^26x)] x>2
= lim arctan[(x+2)(x2)]/[3x(x2)]
=lim arctan[(x+2)]/[3x]
= lim arctan(2/3)
now use your calculator, set to radian mode, to find
lim arctan[(x^2  4)/(3x^26x)] x>2
= .588 
thanks for the reply... the question asks me to evaluate the limit using continuity, how do i justify my answer with continuity?